If Sarah partners Luis in dance 3, which one of the following is a complete and accurate list of the girls any one of...

shunhe on April 21, 2020

Hi @maggsll,

Thanks for the question! This one is definitely a tricky one, so let’s dive into it. First, we know that three boys and three girls are going to give a dance recital, KLM and RST respectively. There are also 3 dances, 1 2 and 3. The children will be partnered by gender for each dance. We can diagram this as following:

R: _ _ _?S: _ _ _?T: _ _ _

Where the slots are for dances 1, 2, and 3. Now take a look at the first rule. We know that K is with S in dance 1 or 2, so we can fill in those two slots:

S: K/ /K _

Now for rule 2: whoever partners R in dance 2 must partner S in dance 3. We can draw a double-sided arrow linking those slots.

Now for the last rule: No 2 children can partner each other in more than one dance. This is one that can combine with rule 2 to tell us that whoever is with R in dance 2 and S in dance 3 is with T in dance 1.

We also know that the person who dances with R in dance 1 has to partner with T in dance 3, meaning he has to partner with S in dance 2.

Finally, we know that the last boy has to partner with S, then T, then R. ?
Hope this helps! Feel free to ask any other questions that you might have.

Xiao on February 17, 2021

@Shunhe

Hi Shunhe, why would you draw a double-sided arrow for this conditional rule? I tested it out that it is indeed a double arrow but I find it difficult to articulate a rule for this scenario so that I can quickly infer that this is not so much of a SA>NA conditional rule situation. Thank you in advance for your explanation!

"Now for rule 2: whoever partners R in dance 2 must partner S in dance 3. We can draw a double-sided arrow linking those slots."